具有外部干扰的不稳定剪切梁的输入–状态稳定  

Input-to-state stabilization of a destabilized shear beam with external disturbances

作　　者：张涵雯 王军民 ZHANG Han-wen;WANG Jun-min(School of Automation and Software Engineering,Shanxi University,Taiyuan Shanxi 030006,China;School of Mathematics and Statistics&Key Laboratory of Mathematical Theory and Computation in Information Security,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]山西大学自动化与软件学院,山西太原030006 [2]北京理工大学数学与统计学院&信息安全的数学理论与计算工业和信息化部重点实验室,北京100081

出　　处：《控制理论与应用》2023年第8期1339-1348,共10页Control Theory & Applications

基　　金：国家自然科学基金项目(62073037,12131008)资助.

摘　　要：本文针对一端受到范德华力的不稳定剪切梁方程,考虑其输入–状态稳定性问题.通过可逆变换把方程等价地变成一个具有反馈循环的2×2的一阶运输方程与常微分方程的耦合系统.通过自抗扰控制方法,给出具有时变增益的扩张状态观测器来估计干扰.应用Backstepping变换和干扰估计量,设计系统的反馈控制来补偿系统本身的不稳定以及消除匹配干扰.通过C0–半群方法证明闭环系统的适定性,以及Lyapunov方法证明闭环系统的输入–状态稳定性.数值仿真验证理论结果的正确性.In this paper,the input-to-state stabilization of an unstable shear beam with van der Waals forces at one end is considered.Through an invertible transformation,the equation is transformed into a 2×2 system of first-order transport equations,which convects in opposite directions cascaded with an ordinary differential equation(ODE).Using the active disturbance rejection control(ADRC)method,an extended state observer with the time-varying gain is given to estimate the disturbance.Applying the backstepping transformation and the disturbance estimation,the feedback control of the closed-loop system is proposed to compensate for the instability of the system itself and cancel the matched disturbance.By the C0-semigroup method and the Lyapunov method,the well-posedness and the input-to-state stability(ISS)of the closed-loop systems are proved,respectively.The validity of the theoretical results is verified by numerical simulations.

关 键 词：不稳定剪切梁方程 反馈控制 自抗扰控制方法 输入–状态稳定性 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]